Effects of normal acceleration on transient burning-rate ...

N A S A TECHNICAL NOTE

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EFFECTS OF NORMAL ACCELERATION ON TRANSIENT BURNING-RATE AUGMENTATION OF A N ALUMINIZED SOLID PROPELLANT .

L

\ '/ \ I by G. Bnrton Northum ' . I

Lungley Reseurch Center Humpton, Vu. 23365

-6625 -

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. APRIL 1972

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NASA TN D-6625 4. Title and Subtitle

EFFECTS OF NORMAL ACCELERATION ON TRANSIENT

SOLID PROPELLANT BURNING-RATE AUGMENTATION OF AN ALUMINIZED

7. Author(s)

G. Burton Northam

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NASA Langley Research Center Hampton, Va. 23365

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National Aeronautics and Space Administration Washington, D.C. 20546

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5. Report Date April 1972

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L-7847 10. Work Unit No.

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a thesis entitled "Acceleration Induced Transient Burning-Rate Augmentation of an Aluminized Solid Rocket Propellant" submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering, Virginia Polytechnic Institute, Blacksburg, Virginia, June 1969.

~- 6. Abstract

Instantaneous burning-rate data for a polybutadiene acrylic acid (PBAA) propellant, containing 16 weight percent aluminum, were calculated from the pressure histories of a test motor with 96.77 cm2 (15 in2) of burning a rea and a 5.08-cm-thick (2.0 in.) propellant web. Additional acceleration tests were conducted with reduced propellant web thicknesses of 3.81, 2.54, and 1.27 cm (1.5, 1.0, and 0.5 in.). The metallic residue collected from the various web thickness tests was characterized by weight and shape and correlated with the instantaneous burning-rate measurements. Rapid-depressurization extinction tests were conducted in order that surface pitting characteristics due to localized increased burning rate could be correlated with the residue analysis and the instantaneous burning-rate data.

The acceleration-induced burning-rate augmentation was strongly dependent on propellant distance burned, o r burning time, and thus was transient in nature. extinction tests and the residue analyses indicate that the transient ra te augmentation was highly dependent on local enhancement of the combustion zone heat feedback to the surface by the growth of molten residue particles on o r just above the burning surface. The size, shape, and number density of molten residue particles, rather than the total residue weight, determined the acceleration-induced burning-rate augmentation.

The results from the

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Acceleration Propellant burning rate Spin-stabilized rockets

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I

EFFECTS OF NORMAL ACCELERATION ON TRANSIENT BURNING-RATE

AUGMENTATION OF AN ALUMINIZED SOLID PROPELLANT*

By G. Burton Northam Langley Research Center

SUMMARY

This paper presents experimental results on the transient burning-rate augmentation of a polybutadiene acrylic acid (PBAA) propellant, containing 16 weight percent aluminum, burned in a 5.08-cm (2.0 in.) web slab motor at pressure levels from 2.07 to 8.27 MN/m2 (300 to 1200 psia) with normal centrifugal accelerations from Og to 140g. The metallic residue retained in similar motors with incremental propellant web thicknesses was correlated with (1) the burning-rate data and (2) geometrical characterizations of the pitted propellant surface obtained from extinction tests at different burn times and acceleration levels.

The normal-acceleration-induced burning-rate augmentation at a given pressure was strongly dependent on (1) acceleration level and (2) distance of propellant burned (or burning time). This transient ra te augmentation was caused by increased localized burning rates resulting from local enhancement of the combustion zone heat transfer to the surface by the growth of molten residue particles retained just above the burning sur - face. The transient size, shape, and number density of the particles on the surface, rather than the total residue weight, determined the acceleration-induced burning-rate augmentation.

INTRODUCTION

Many solid-propellant rocket vehicles have been developed that use spin for inertial stabilization and for reducing dispersion due to thrust misalinement in flight. Spin- induced effects on some rocket motors with metallized propellants have led to increases in propellant burning rate, motor chamber pressure, and chamber heating. These phenomena are the result of centrifugal loading effects on the combustion process and spin- induced vortex flow effects in the combustion chamber and nozzle.

The information presented herein was included in a thesis entitled "Acceleration- Induced Transient Burning-Rate Augmentation of an Aluminized Solid Rocket Propellant" submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering, Virginia Polytechnic Institute, Blacksburg, Virginia, June 1969.

*

From a review of the literature (refs. 1 to 14), several qualitative statements can be made concerning the effects of aluminized propellant formulation variables and ballis- t ics on the sensitivity of the propellant burning rate to acceleration environments:

(1) The burning-rate augmentation varies with acceleration level depending on the propellant and is a strong function of the orientation of the acceleration vector. This effect is largest when the acceleration vector is normal into the burning surface.

(2) Although the rate augmentation generally decreases with decreased aluminum particle size and aluminum percentage, in many cases it depends on the propellant system and acceleration level. Reduction of the oxidizer particle size also decreases the burning-rate augmentation.

(3) No consistent pressure dependence of ra te augmentation was observed for the wide variety of propellants that have been tested.

(4) The propellant static test burning rate appears to be the best index for predicting the sensitivity of solid propellants to acceleration loads.

(5) The rate augmentation is transient and, thus, also varies with burning time or propellant distance burned.

To date the characterization of the transient ra te augmentation has been limited by one o r more of the following experimental and analytical constraints: (a) the use of small propellant strands which produce unrealistic edge effects, (b) the use of thin-web test motors that do not have sufficient propellant web thickness to allow the rate augmentation to reach a quasi-equilibrium value, and (c) the use of long time-average augmentation as a measure of the effect.

The subject investigation was conducted to characterize the transient burning-rate augmentation of an aluminized composite solid propellant subject to acceleration forces normal into the burning surface and to elucidate the mechanisms of burning-rate augmentation due to the imposed acceleration force. Since previous results (refs. 3 and 11) indicated increased weights of metallic residue with increasing acceleration level, particular attention was directed toward correlation of the calculated instantaneous rate data with the metallic fuel residue remaining at motor burnout. The propellant web thickness was varied in order that this residue could be collected and correlated with distance of propellant burned.

SYMBOLS

Values a r e given in both SI and U.S. Customary Units. The measurements and cal- culations were made in U.S. Customary Units.

2

A

At a

DB

dt,f

dt,i

K

n

r0

rt

rt,max

t

tb

growth constant in equation (4)

throat area

burning-rate constant

dis tanc e burned

final throat diameter

initial throat diameter

ratio of burning surface to throat area

pressure exponent

pres sur e

average pressure

reference pressure in rate equation

instantaneous chamber pressure

burning rate

average burning rate

Rate under acceleration Static rate at same pressure

burning-rate augmentation,

static test burning rate

instantaneous burning rate

maximum instantaneous burning rate

time

pressure burn time

3

initial time to burn time ti

W residue weight

W Total residue weight Burning surface area specific residue weight,

a n normal acceleration into burning surface

6 initial propellant thickness

Number mean pit diameter is defined as midpoint on diameter-number-percent- distribution curve.

Pit density is the number of pits per unit area.

APPARATUS AND PROPELLANTS

Centrifuge

The centrifuge at the Langley Research Center was previously used as described in reference 11. It was modified for this study to increase the rotational radius to the propellant surface from 1.14 to 2.03 m (45 to 80 in.). A photograph of the modified centrifuge with a test motor mounted on each a r m is shown in figure 1. The motor shown on the right side of the photograph includes the extinction apparatus which is described in a later section. The test motor was mounted on the centrifuge in a manner that eliminated rotational speed changes due to motor thrust. The increase in acceleration due to regres- sion of the 5.08-cm-thick (2.0 in.) propellant web from an initial radius of 2.03 m (80 in.) was 2.5 percent. The rotational speed of the centrifuge was measured with a 60 pulse/revolution tachometer and a pulse counter. The centrifuge was brought to the desired speed before the rocket test motor was ignited.

Test Motor

The unidirectional-burning slab motor shown in figure 2 was utilized to minimize the effects of propellant grain geometry and spin-induced vortex flow so that the transient burning rate could be investigated in a nearly uniform acceleration environment. The lower inser t on which the propellant slab was bonded and the upper inser t that formed the top of the rectangular gas port were within the cylindrical pressure vessel. All propellant slabs used in the motor were 6.9 cm (2.7 in.) wide by 13.7 cm (5.4 in.) long. A steel spacer plate was used under thinner slabs c5.08 cm (<2.0 in.) to maintain the propellant

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surface in the same location with respect to the igniter gas ports as the web thickness was reduced in 1.27-cm (0.5 in.) increments.

Two ports were machined in the head-end plate to provide for chamber pressure measurements. Strain-gage pressure transducers were connected to the pressure ports with 0.64-cm (1/4 in.) stainless-steel tubing. Various nozzle throat diameters were used to obtain the desired high, medium, and low pressure levels.

Extinction Test Apparatus

A blowoff nozzle and water quench system were employed so that the propellant could be partially burned while spinning, then extinquished, and examined for surface geometry changes. The test motor nozzle assembly was modified to accept two 0.64-cm- diameter (0.25 in.) explosive bolts for release of a plate holding the graphite nozzle insert. When the explosive bolts were activated during motor burning, the motor throat a rea was rapidly increased and a solenoid valve released a small amount of water into the chamber through the modified head-end plate and upper insert. The water cooled the chamber and prevented reignition. These modifications to the test motor a r e not shown in figure 2 for the sake of clarity.

Propellant

Three batches of aluminized polybutadiene acrylic acid (PBAA) propellant were used during the investigation. The propellant formulation and physical properties are given in table I. The static burning-rate data from the three propellant batches were least-squares fitted to the equation r = a p pref)n. The calculated burning-rate constant a was 7.80 mm/sec (0.307 in./sec) and the pressure exponent n was 0.255 when

was 3.45 MN/m2 (500 psia). The reproducibility of these data indicated that batch- P r ef to-batch variations in burning rate should not have affected the test results.

( /

PROCEDURE

Test Procedure

The motors were fired at the test cell ambient temperature which was maintained at 21' f 3 O C (700 f 5O F). After motor burnout, the centrifuge was gradually stopped. Each test motor was disassembled and the lower inser t and the nozzle were examined. Any remaining metallic residue from the lower inser t was collected in a plastic bag and placed in a desiccator until analysis could be performed.

Since the magnitude of the burning-rate increase due to the imposed acceleration was unknown, the nozzle throat diameter required to give the desired average operating pressures could not be determined until a preliminary burning-rate-acceleration rela-

5

tionship had been defined. In order that tests could be conducted at nominal average chamber pressures of 2.07, 4.14, 6.21, and 8.27 MN/m2 (300, 600, 900, and 1200 psia), high and low pressure tests were f i r s t conducted at each of the seven normal acceleration levels from Og to 140g ( lg = 9.8 m/sec2) in 20g increments with the nozzle throat diameters sized from the K-p curve obtained from static tests. (The K-p curve is a plot of the ratio of the burning surface a rea to the nozzle throat area as a function of the average chamber pressure.) The static curve was established by using estimated nozzle throat sizes. These initial tes ts were used to generate a K-p curve for each acceleration level, from which the throat diameters for the desired pressure levels could then be calculated.

Variable web thickness tests were conducted at the medium pressure for each acceleration. The initial portion of the pressure histories with variable propellant web thicknesses was reproduced, even though the average pressure changed because of the dependence of burning rate on propellant distance burned under acceleration conditions.

The extinction tes ts were conducted in a manner similar to the other acceleration tests, except that, at a preprogramed time during motor burning, the explosive bolts and the water control solenoid were electrically activated.

Data Reduction

Since there was no available means of measuring instantaneous propellant burning was calculated from the pressure time history rate, the instantaneous burning rate rt

and motor characteristics by equating the mass flow from the burning surface to the nozzle discharge obtained from the average discharge coefficient for a given test. The equation

At6Pt rr. =

was employed to include the effects of nozzle erosion. Nozzle erosion was assumed to be exponential; therefore, the throat a r ea At was defined as

At = 2 4 dt,? +:(It,: - dtYi2)t e x p k - 1) where dt i and dt,f were the initial and final throat diameters, respectively.

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The propellant distance to obtain

r t

burned to t ime t was calculated by integrating equation (1)

The test motor performance characteristics based on pressure burn t ime were calculated and listed; then the instantaneous pressure, instantaneous burning rate, and distance burned were calculated and tabulated at 0.040-sec intervals. The instantaneous chamber pressure and rate data were then plotted (for each acceleration level) with distance burned as a parameter. Thus, the burning rate could be interpolated for fixed values of acceleration, pressure, and distance burned. An example of the instantaneous rates is shown in figure 3 for the 140g acceleration level. The instantaneous rates at ignition and burnout were not used because of the highly transient nature of these processes.

The burning ra tes shown in figure 3 a r e typical data. The complete data tabulation is shown in table II. (The rt data from a single motor firing are shown as solid symbols in fig. 3.) The lines represent the least-squares f i t of the data. Values of a and n for all experimentally determined burning rates are given in table 111 for pref = 3.45 MN/m2 (500 psia). tance burned for the nominal average pressure values. remainder of this report are based on these values.

These correlations were then used to obtain values of burning rate and dis- The curves presented in the

The accuracy of calculated rt was spot checked by comparing the average rate computed from the calculated instantaneous data with F based on pressure burn time and measured web thickness. all points randomly checked. e te rs used to calculate rt, the rt data should be accurate to *2 percent.

There was less than 0.5 percent difference in the rates of Because of the care taken to accurately measure the param-

Residue Analysis

The metallic residue that was retained on the lower insert of the burned-out motors by the acceleration force was carefully collected. The residue was analyzed to determine the general shape of the particles. Before the analysis the particles were washed with methyl ethyl ketone on a 100-mesh screen to separate the carbonaceous material resulting from the liner char from the metallic Al/A1203 residue. particles retained on each sieve was identified along with the weight retained. The shapes were categorized as spheres, buttons, irregular agglomerates, and sheets. In order to

The characteristic shape of the

7

I 1 l 1 1 l l I

determine the transient-residue characteristics, motors were tested with propellant web thicknesses of 1.27, 2.54, and 3.81 cm (0.5, 1.0, and 1.5 in.) i n addition to the 5.08-cm (2.0 in.) web used for the burning-rate data. The residue collection tests were conducted with the nozzle throat diameters used for the medium pressure 4.14-MN/m2 (600 psia) 5.08-cm (2.0 in.) web tests. Two firings were conducted at each web thickness and at each of the test accelerations. Additional tests were conducted at 140g to determine the effect of pressure on the residue remaining from the 5.08-cm (2.0 in.) web motor. It was real- ized that the residue remaining at motor burnout may differ from that retained on the burning propellant surface. (See ref. 8.) However, the change in the residue character- ist ics with distance burned and acceleration was an available means of investigating the complex combustion phenomena associated with acceleration-induced transient burning- rate augmentation of the aluminized propellant. The specific residue weight was defined as the total residue weight divided by the propellant burning surface area.

Extinction Test Analysis

Photographs of the pitted propellant surface were made and the pit diameters and number density of 25.8 cm2 (4.0 in2) of the propellant surface were measured from the photographs by use of a Zeiss TGZ-3 Particle-Size Analyzer. The diameters reported are approximate because the exact edge of the pit was not always well defined in the photographs. The number mean pit diameters a r e reported at a given test condition. Num- ber mean pit diameter is defined as the midpoint on a diameter-number-percent- distribution curve.

DISCUSSION OF RESULTS

Tests were conducted to determine the effects of normal acceleration into the propellant on the burning-rate augmentation, on the retention of metallic residue, and on the condition of the propellant surface following extinction. The results from these three areas are presented followed by "Correlation of Results. *' The transient burning-rate data were analyzed as a function of propellant distance burned rather than burning time. This procedure facilitated correlation of the residue data from motor firings having variable propellant web thicknesses with the transient-burning rate data.

Burning Rate

Typical pressure histories for motors that had nozzles sized for average chamber pressures of 4.14 MN/m2 (600 psia) are shown in figure 4 for several accelerations. These traces cannot be compared directly since the throat area was changed to maintain the average pressure as the acceleration level was increased.

8

The 5.08-cm (2.0 in.) web motors were tested at each acceleration level from Og to 140g normal acceleration in 20g increments to determine the rate augmentation. The average burning-rate augmentation (r/ro)av based on tb and the maximum rate augmentation ( r / r o ) m u (the maximum instantaneous rate divided by static rate) at 3.45 MN/m2 (500 psia) were plotted as a function of acceleration level in figure 5. The largest change in rate augmentation occurred at lower accelerations between 20g and 60g. The decreased sensitivity of the average rate augmentation indicates a saturation of the mechanism causing the burning-rate augmentation with increasing acceleration level. Similar results were previously observed in 1.27-cm '(0.5 in.) web test motors with a similar propellant (ref. 11).

The instantaneous burning rates rt, calculated as discussed in the procedures, are shown in figure 6. The rt data at DB = 2.54 mm (0.10 in.) and zero normal acceleration were used as the initial burning rates for the acceleration tests. This procedure eliminated ignition transient effects by assuming that for small distances burned, the burning rate under acceleration was equal to the static rate. The symbols with ticks in figures 6(b) to 6(h) at DB = 50.8 mm (2.0 in.) a r e the static r t data at DB = 48.3 mm (1.9 in.) from figure 6(a). These data points were included as reference points to indicate the increased rate due to the acceleration environment. The unidirectional-burning slab motor was designed to give neutral burning pressure time histories. However, the rates shown in figure 6(a) for the static or nonspin tes ts indicate a slight increase in calculated burning rate rt of 8 percent with increasing DB. This variation did not adversely affect the conclusions , since the acceleration-induced rates were much larger than this variation.

At accelerations of 20g and 40g (figs. 6(b) and 6(c)) the instantaneous burning rates

rt 60g and 80g (figs. 6(d) and 6(e)), rt increased, passed through a maximum, and then continued to decrease until motor burnout. and 6(h)), rt increased to a maximum, decreased, and then leveled off somewhat as DB increased. At accelerations of 40g, 60g, and 80g the 5.08-cm (2.0 in.) web was not sufficient to permit achievement of the quasi-equilibrium rate observed at the higher accelerations.

increased with increasing distance burned. When the acceleration was increased to

At accelerations of lOOg to 140g (figs. 6(f), 6(g),

Figure 7 shows a composite of the curves for rt plotted against DB at 4.14 MN/m2 (600 psia) which allows comparison of the changes in transient burning rate with increasing acceleration level at this pressure.

The maximum rate and the distance burned to achieve rt," are shown in figures 8 and 9, respectively, as a function of acceleration with pressure as a parameter. Figure 8 shows that rt,max increased with increasing acceleration up to 1OOg. Figure 9 illustrates the decreasing distance burned to achieve rt,mu with increasing accelera-

9

tion. At 20g, rtYmax occurred near motor burnout, whereas at 140g it occurred much earlier, DB = 15.24 mm (0.60 in.). The distance burned to r t , m z showed no strong dependence on pressure, except at the 60g acceleration level.

Figure 10 shows the variation in rt at a distance burned of 48.3 mm (1.9 in.) as a function of normal acceleration with pressure as a parameter. The curves were drawn through the data points that indicated quasi-equilibrium burning rates with respect to DB. The data points with arrows indicate that rt had gone through a maximum, was decreasing, but had not reached a constant rate at motor burnout.

In the quasi-equilibrium region, rt is essentially independent of distance burned. Thus it may be possible to use the curves in figure 10 to predict the quasi-equilibrium burning rate for values of distance burned beyond 48.3 mm (1.9 in.) at a given acceleration. If this prediction method could be shown to hold, one could, with confidence, use similar subscale data to predict the performance of operational motors with greater web thickness. scale acceleration testing and should be explored more fully.

The technique has the obvious advantage of avoiding the cost of extensive full-

The acceleration-induced rate augmentation was dependent on chamber pressure as shown parametrically in figure 6. mentation with increased chamber pressure a r e shown in figure 11 for the 140g acceleration level. At 2.07 MN/m2 (300 psia) the maximum burning-rate augmentation was 1.23. The burning-rate augmentation increased to 1.42 when the pressure was increased to 8.27 MN/m2 (1200 psia). It was concluded that increased burning-rate augmentation with increased pressure resulted from improved aluminum combustion efficiency at the higher pressure level as evidenced by a decrease in the weight of metallic residue retained (to be presented in a later section).

Typical data indicating the increased burning-rate aug-

Residue Analysis

Results from ear l ier extinction tests (ref. 11) of partially burned 1.27-cm (0.5 in.) web motors indicated the presence of metallic residue in pits formed on the propellant surface. It was concluded that the presence of the metallic residue was one cause of the average burning-rate augmentation observed.

During the subject investigation, the metallic residue retained on the lower inser ts of the burned-out motors by the centrifugal acceleration force was collected and analyzed for correlation with the acceleration-induced burning-rate augmentation. Figure 12 illus- t ra tes the variation of total residue weight W and specific residue weight w as a function of propellant web thickness for various accelerations. The results of the residue classification are indicated at the top of each figure as weight percent of the indicated geometry. The percentages encircled denote the classification of the majority of the residue at a given web thickness.

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The changes in residue characteristics with distance burned indicate the transient nature of the residue growth process at a given acceleration. For the lower accelerations the majority of residue remained spherical as the web thickness increased to 5.08 cm (2.0 in.). At 80g, the residue was mostly spherical for webs of 2.54 cm (1.0 in.) or less , after which buttons and irregular particles formed with increased distance burned.

As the acceleration level was increased, sheets of residue formed. The percentage of sheeted residue at a given web thickness increased and the distance burned to produce the sheets was reduced with increased acceleration level. reference 7 data which suggested that the propellant surface becomes flooded when sufficient residue has been retained.

Thus, the data substantiated

Figure 13 illustrates the variation in residue weight and characteristics for the 5.08-cm (2.0 in.) web motor tests as a function of normal acceleration. The residue weight increased exponentially with acceleration. At 140g, 1.71 percent of the nominal propellant slab weight was retained. As the acceleration level increased, the residue character progressed from spherical particles to sheets of residue covering the lower insert. both acceleration and distance burned.

Thus, the flooding of the burning surface with sheets of residue was a function of

A composite semilogarithmic plot of the average residue weight and specific residue weight a r e shown in figure 14 as a function of distance burned. nearly exponential growth in residue weight with increasing distance burned. indicate that the residue weight retention process can be described by the first-order kinetic equation

Figure 14 shows the The data

dW - = AW dDB

(4)

which represents a "collision" process where the growth rate dW/dDB depends on the amount of residue present. The growth constant A was not strongly acceleration dependent. The growth process is consistent with the collision reasoning as long as the residue does not cover the major fraction of the burning surface. Results from the extinction tests (discussed in the next section) indicated discrete pits at large values of DB in regions where the residue data indicated sheeting. The results of films taken of similar propellants (ref. 2) indicate discrete molten agglomerates retained on burning surface with a progression from spherical particles to shallow pools. Thus, the molten residue may retain its discrete particulate nature, with increasing particle diameter on o r above the burning surface, and the sheeting result from agglomeration of these particles at motor burnout.

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The average residue weight at DB = 50.8 mm (2.0 in.) is shown in the semilogarithmic plot of figure 15. This figure illustrates the exponential increase in residue weight with increasing acceleration. An explanation of the exponential dependence of residue weight on normal acceleration was not attempted.

The effect of pressure on residue weight was examined by firing additional 5.08-cm (2.0 in.) web motors at elevated and reduced pressure levels at 140g. the results of these tests. Although there was scatter in the residue data, the weight retained decreased with increasing average motor pressure. The residue weight decreased by a factor of 2.5 as the pressure was increased from 1.04 to 7.59 MN/m2 (150 to 1100 psia).

Figure 16 shows

Extinction Tests

In order to gain better understanding of the effect of the retention of metallic res i - due on or above the burning propellant surface, the test motor was modified such that the propellant could be extinguished after burning for various times at selected acceleration levels. The propellant surface could then be examined for changes in pit characteristics.

Photographs of the resultant propellant surface from extinction tests conducted with the medium pressure nozzle at the time of peak pressure o r largest burning rate are shown in figure 17 for normal accelerations of Og, 40g, 60g, 80g, lOOg, and 120g. The 140g photograph is shown as one of the ser ies of photographs in figure 20. No figure is shown at 20g since its surface was similar to the smooth surface obtained from the Og normal acceleration test.

Figure 17 shows that as the acceleration level was increased to 40g, the propellant surface became pitted. When the acceleration level was further increased, the pit diameter became limited by and decreased with increased pit density (number of pits per unit area).

The approximate number mean pit diameters and pit densities were measured and the results from the analysis a r e shown in figure 18. The photograph at 40g (fig. 17) showed both large and small pits. At 40g, the mean diameter for each of the distributions as well as the maximum diameter a r e shown to indicate the variation obtained. Above 80g the mean pit diameter decreased slightly with increasing acceleration level as shown in figure 18.

The increased number of pits and the decreased pit size with increasing acceleration at the peak burning rate indicate that the residue retained just above the burning surface caused some cases

localized increased burning rates in the vicinity of the residue particles. In residue particles remained in their pits during extinction.

12

. . .

Figure 19 compares the pressure history from a 5.08-cm (2.0 in.) web test and the pressure histories resulting from the extinction tests with the same nozzle s ize at 140g. decreasing, and in the quasi-equilibrium region following the decline. the pressure histories in the figure also illustrates that the transient burning-rate augmentation was very reproducible.

Extinction tests were conducted when the pressure was increasing, at a maximum, The agreement in

Figure 20 shows photographs of extinguished propellant surface as a function of selected calculated distance burned or burning time at 140g. The result of the Og normal acceleration extinction test is also shown in figure 20 for comparison.

There was a gross change in the resultant propellant surface as a function of distance burned. The pit diameter increased, and the pit density decreased with increased distance burned. This drastic change in propellant surface indicated the transient effect of the metallic residue on the local burning rate.

The number mean pit diameter and pit density were plotted as a function of distance burned in figure 21. The pit diameter increased almost linearly with DB. The pit density decreased exponentially with increasing DB. This change in pit characteristics as a function of DB indicates that any proposed local burning-rate model should include the acceleration-induced transient burning-rate augmentation by including time o r distance- dependent pitting characteristics.

Clayton T. Crowe of Washington State University has extended the United Technology Center (UTC) local heat feedback model to predict the reduction in r/ro as the spherical residue particles grow to become more platelet shaped. The model is in agreement with the limited data available. The UTC model also predicts the observed behavior of r/ro on n, p, and ro. The lack of transient residue growth and accumulation models severely limits the prediction of r/ro using the current heat feedback models.

The relatively large mean pit diameters experienced indicate that caution should be exercised in the use of small strands to evaluate acceleration effects on solid-propellant burning rate since the a rea of a single pit can be on the order of the burning surface area.

Correlation of Results

The instantaneous burning-rate data and the residue data given in figures 6 and 12 were examined for correlation between the residue growth process and the acceleration- induced transient burning-rate augmentation. Two acceleration levels were chosen for presentation, although the discussion herein w a s found to apply at all acceleration levels. The 80g and 140g data were selected because these data were typical of the two types of instantaneous rate data observed, that is, at 80g the burning rate increased, gradually reached a maximum at DB = 25.4 mm (1.0 in.), and continued to decrease until motor

13

burnout; at 140g the burning rate increased rapidly, reached a maximum at DB = 15.2 mm (0.6 in.), decreased, and then continued at a quasi-equilibrium rate independent of DB.

The instantaneous burning rate at 4.14 MN/m2 (600 psia), the residue weight, and the residue shape characteristics are shown in figure 22 for the 80g and 140g acceleration levels as a function of distance burned. In all cases the point of maximum burning rate corresponded to a distance burned where the majority of the residue particles were spherical. The burning rate was observed to have passed through the maximum and to be decreasing when the residue analysis indicated that the spherical particles had progressed to buttons. The quasi-equilibrium rate coincided with the formation of sheeted residue. Although the residue weight increased exponentially with distance burned, only a portion of the total residue was associated with the maximum burning-rate augmentation (fig. 22) except at the lower acceleration where the maximum rt occurred near burnout. These data and the photographs from the extinction tests indicate that the transient burning-rate augmentation results from local burning-rate increases controlled by the residue particle characteristics and number density rather than total residue weight. Thus the growth characteristics of the residue, as aluminum becomes available at the receding surface, correlates the acceleration-induced transient burning-rate augmentation.

CONCLUDING REMARKS

The acceleration-induced transient burning-rate augmentation of a polybutadiene acrylic acid (PBAA) propellant containing 16 weight percent of aluminum was characterized at 2.07 to 8.27 MN/m2 (300 to 1200 psia) with nearly constant centrifugal accelerations from Og to 140g normal into the burning surface. Instantaneous burning-rate data were calculated from the pressure histories of a test motor with 96.77 cm2 (15 in2) of burning area and a 5.08-cm-thick (2.0 in.) propellant web. Additional acceleration tests were conducted with reduced propellant web thicknesses of 3.81, 2.54, and 1.27 cm (1.5, 1.0, and 0.5 in.). The metallic residue collected from the various web thickness tests was characterized by weight and shape and correlated with the instantaneous burning- rate measurements. Rapid-depressurization extinction tests were conducted in order that surface pitting characteristics due to localized increased burning rate could be correlated with the residue analysis and the instantaneous burning-rate data.

The acceleration-induced burning-rate augmentation was strongly dependent on propellant distance burned, or burning time, and thus w a s transient in nature. The results from the extinction tests and the residue analyses indicate that the transient ra te augmentation was highly dependent on local enhancement of the combustion zone heat feedback to the surface by the growth of molten residue particles on or just above the burning

14

surface. the total residue weight, determined the acceleration-induced burning-rate augmentation.

The size, shape, and number density of molten residue particles, rather than

Langley Research Center, National Aeronautics and Space Administration,

Hampton, Va., February 14, 1972.

15

REFERENCES

1. Manda, Leo J.: Compilation of Rocket Spin Data. Vol. 11: Literature Survey. Rep. No. 3001-2 (Contract No. NAS1-6833), Electron. & Space Div., Emerson Elec. Co., July 22, 1968. (Available as NASA CR-66641.)

2. Willoughby, P. G.; Baker, K. L.; and Hermsen, R. W.: Photographic Study of Solid Propellants Burning in an Acceleration Environment. Contract No. "1-8796, United Technol. Center. (Available as NASA CR-66824.)

3. Willoughby, Paul G.; Crowe, Clayton T.; Dunlap, Roger; and Baker, K. L.: Investiga- tion of Internal Ballistic Effects in Spinning Solid Propellant Motors. UTC 2281-FR (Contract No. N00017-67-C-2429), United Technol. Center, Oct. 1968. from DDC as AD 847 282.)

(Available

4. Burchard, J. K.; Hermsen, R. W.; Dunlap, R.; Lee, J. T.; and Willoughby, P. G.: Investigation of Performance Losses and Ballistics Effects in Solid Propellant Rockets. UTC 2197-FR (Contract No. NOW 66-0444-c), United Technol. Center, Apr. 14, 1967. (Available from DDC as AD 815 115.)

5. Crowe, C. T.; Willoughby, P. G.; Dunlap, R.; and Hermsen, R. W.: Investigation of Particle Growth and Ballistic Effects on Solid Propellant Rockets. UTC 2128-FR (Contract No. NOW 65-0222-f), United Technol. Center, June 15, 1966. (Available from DDC as AD 486 262.)

6. Bulman, M. J., and Netzer, D. W.: Burning Rate Acceleration Sensitivity of Double- Base Propellant. AIAA J., vol. 8, no. 6, June 1970, pp. 1155-1156.

7. Sturm, E. J.; and Reichenbach, R. E.: Aluminized Composite Solid-Propellant Burn- ing Rates in Acceleration Fields. AIAA J., vol. 7, no. 11, Nov. 1969, pp. 2087-2093.

8. Anderson, J. B.; and Reichenbach, R. E.: An Investigation of the Effect of Accelera- tion on the Burning Rate of Composite Propellants. AIAA J., vol. 6, no. 2, Feb. 1968, pp. 271-277.

9. King, M. K.; and McHale, E. T.: An Optical Bomb Study of the Combustion of Solid Propellants in High Acceleration Fields. Contract No. N00014-67-C-0455, Atlantic Res. Corp., Mar. 1970. (Available from DDC as AD 508 083.)

10. Northam, G. B.; and Lucy, M. H.: Effects of Acceleration Upon Solid-Rocket Per- formance. J. Spacecraft Rockets, vol. 6, no. 4, Apr. 1969, pp. 456-459.

11. Northam, G. Burton: Effects of Steady-State Acceleration on Combustion Character- ist ics of an Aluminized Composite Solid Propellant. NASA TN D-4914, 1968.

16

12. Northam, George Burton: An Experimental Investigation of the Effects of Accelera- tion on the Combustion Characteristics of an Aluminized Composite Solid Propel- lant. M.S. Thesis, Virginia Polytech. Inst., 1965.

13. Glick, Robert L.: An Analytical Study of the Effects of Radial Acceleration Upon the Combustion Mechanism of Solid Propellant. Rep. No. 42-66 (Contract NAS7-406), Thiokol Chem. Corp., Dec. 1966. (Available as NASA CR-66218.)

14. Whitesides, R. Harold, Jr.; and Hodge, B. Keith: Theoretical Study of the Ballistics and Heat Transfer in Spinning Solid Propellant Rocket Motors. U-68-20A (Con- tract No. NAS 1-7034), Thiokol Chem. Corp., Aug. 1968. (Available as NASA CR-66639.)

17

TABLE I.- PROPELLANT FORMULATION AND PHYSICAL PROPERTIES

191

9 1

191

Composition

400 0.876

200 .876

400 1.034

~

Ingredients

PBAA binder

Oxidizer Coarse ammonium perchlorate Fine ammonium perchlorate

Aluminum powder

Batch no. k

Weight, percent

14

70 45.5 24.5

16

Comments

Includes curing agent, Thiokol HA polymer

180 p m weight median diameter 20 p m weight median diameter

7 p m weight median diameter; i r regular shape

Physical properties at 240° C (70° F)

Batch s ize I Maximum stress

kg I lb I MN/m2 psi

Static burning rate

r = a(P/P,ef)n

127

127

150

Strain at maximum stress, percent

27

28

26

a = 7.80 mm/sec (0.307 in./sec)

n = 0.255

pref = 3.45 MN/m2 (500 psia)

18

TABqE U.- BURNING-RATE DATA

(a) SI unlts

Pres~ures and burlllng rales for dlstance burned of - 10.16

P. IN/m2

2.519 5.881 4.210 4.144 5.829 1.958

2.206 2.311 4.061 4.000 6.136 6.812

2.350 2.460 3.654 3.615 5.709 7.143

2.062 4.040 3.964 5.592 1.653

2.641 2.006 4.316 3.151 0.516

~

2;& -

2.512 5.911 4.021 4.240 6.143 2.002

2.282 2.413 4.006 4.095 0.184 6.840

2.261 2.599 3.916 3.916 6.150 1.800

2.261 4.213 4.185 6.123 1.081

2.689 2.193 4.247 4.164 6.371 8.600

2.951 2.137 4.261 4.420 7.151 8.818

2.206 2.923 4.137 4.240 7.130 6.681

2.627 2.413 4.185 3.992 6.536 8.660

~

~

~

-

. -

~

-

mm

I, mm/se

7.19 8.14 8.43 1.65 8.59 6.32

6.65 6.68 8.08 0.15 9.25 9.65

1.44 6.06 7.00 8.05 9.21 9.98

6.55 9.19 8.66 9.41

11.20

7.54 6.11 9.30 0.30

11.13

I

-

!m/se'

- 1.26 8.92 8.10 6.13 9.02 6.73

6.99 7.01 8.15 8.43 9.50 9.93

1.21 1.29 8.56 8.64

10.41 11.38

7.34 8.10 9.27

10.57 11.81

1.17 7 .31 9.30 9.42

10.91 12.32

8.20 1.42 9.60 9.70

11.61 12.50

7.44 8.33 9.55 9.91

11.91 11.07

1.07 7.17 9.50 9.27

10.17 12.34

-

-

-

__

-

-

-

-

2.111 4.111 4.640 1.736 0.080

2.324 2.930 4.530 4.606 6.991 1.626

2.985 2.723 4.019 4.576 1.984 m0.103

m

m/se

7.08 8.84 8.03 1.54 8.05 6.10

6.05 0.40 1.59 1.82 8.61 8.56

1.04 6.48 7.32 7.10 8.94 8.14

6.11 0.51' 8.15 8.28 9.98

6.93 6.32 8.06 7.62 8.71 ~

~

6.20 7.67 6.31 0.71 9.42

6.11 6.66 1.01 6.53 9.93 8.69

6.73 0.73 0.26 7.70 6.94 9.37

1.26 9.21

10.11 12.34 14.15

7.77 6.26

10.31 10.67 13.67 12.60

6.76 6.64

10.92 10.57 13.03 14.33

Im

"set

1.06 0.56 8.28 7.65 8.23 6.12

6.20 6.45 7.80 7.95 8.91 9.45

1.26 6.55 1.44 1.60 9.21 9.19

6.11 0.14 8.31 6.38

10.11

1.06 0.32 6.38 1.00 9.35

~

~

6.45 7.98 8.64 9.66

11.10

7.04 7.14 8.79 9.21

12.22 10.80

7.31 7.39 9.19 8.74

11.13 11.61

15.24 mm 20.32 mm im

d 6 . 1

7.31 9.17 8.33 8.38 9.40 6.61

7.19 7.19 8.41 8.69 9.73 0.19

7.20 7.39 8.84 0.01 0.54 2.15

1.62 0.59 0.03 1.99 3.31

6.50 1.90 0.59 0.05 .2.09 R D I

R D I 8.03

0 . 7 1 11.00 13.34 14.71

7.82 9.09

10.44 10.49 12.96 12.09

1.92 1.02 9.60 9.15

11.40 12.13

30.48 mm 35.56 mm 40.64 mm 45.72 mm WXl UlUL

0

20

40

60

80

LOO

120

140

2.5

P. m / m :

2.541 5.964 4.051 3.992 5.585 1.889

2.013 2.234 3.841 3.841 5.895 6.605

2.221 2.351 3.401 3.523 5.536 6.343

1.951 3.602 3.144 4.909 6.801

2.441 1.903 3.165 3.420 5.109 t

t

1.813 3.475 3.813 5.502 6.764

2.006 2.420 3.468 3.696 6.557 5.392

2.282 2.130 3.640 3.331 5.502 6.614

5.01

P. m / m t

2.551 5.771 1.111 4.040 5.709 1.896

2.055 2.248 3.944 3.916 5.985 6.081

2.303 2.365 3.503 3.571 5.136 6.640

1.951 3.033 3.199 4.957 6.950

2.402 1.896 3.896 3.496 5.481

I

~

~

1.866 3.599 3.964 6.095 7.950

2.103 2.537 3.661 4.013 8.046 6.550

2.496 2.330 4.054 3.192 6.640 8.267

25.4

P. nN/m2

2.620 6.151 4.151 4.392 6.426 2.089

2.365 2.415 4.158 4.213 6.351 1.074

2.282 2.013 4.060 4.006 6.310 0.846

2.365 4.026 4.530 6.964 8.929

2.912 2.351 4.854 4.019 7.033 TABU

TABU 2.324 4.105 5.026 6.200

10.315

2.324 3.213 4 5 5 1

4.502 0.446 7.302

2.661 2.441 4.295 4.213 6.936 9.681

48.26 mm

P, IN/m:

2.634 6.033 4.199 4.240 6.136 2.006

2.282 2.392 4.164 4.102 6.214 6.984

2.303 2.530 3.192 3.710 5.820 1.929

2.165 4.289 4.109 6.226 8.536

2.199 2.172 4.602 4.220 7.171

~

~

2.268 4.688 5.116 6.350 0.742

2.461 3.254 4.819 4.806 9.261 7.661

3.013 2.756 4.861 4.751 1.990 0.535

m/se

1.34 8.91 8.30 8.05 8.92 6.53

6.91 6.88 8.33 0.38 9.50 9.93

7.29 1.06 1.65 0.20 9.50

11.20

6.91 9.18 9.02

10.59 12.51

8.00 7.26

10.13 9.45

12.21 - ~

7.00 10.46 11.15 13.36 15.14

0.26 9.19

11.00 11.15 14.12 12.70

6.94 0.79

11.07 10.97 13.00 14.06

~

m/ser

1.21 8.91 1.65 8.33 9.32 1.24

1.39 1.34 8.20 8.71 9.80

10.13

1.16 1.90 9.21 9.45

11.26 12.45

6.10 9.30 9.35

11.18 11.63

1.44 7.41 8.36 9.35

10.62

~

~

~

1.32 9.40 8.66

10.80 11.61

7.01 8.03 0.71 9.32

10.97 10.31

7.67 1.47 6.64 6.69

10.21 11.23

-

m/se

1.14 0.06 7.52 8.23 9.30 1.32

1.39 1.32 8.15 8.11 9.03

10.06

7.14 7.95 9.11 8.91

11.23 12.29

0.10 8.99 9.14

11.00 11.30

7.19 7.52 8.20 9.01

10.44

~

- 1.32 9.27 8.48

10.69 11.38

6.93 7.98 0.64 9.22

10.92 10.24

1.10 1.65 9.04 6.64

10.11 11.13

P. N/m:

2.034 6.129 4.185 4.323 0.350 2.055

2.330 2.448 4.118 4.111 6.357 7.074

2.275 2.592 3.923 3.002 6.081 0.570

2.268 4.509 4.331 6.764 6.906

2.930 2.310 4.902 4.633 7.122 - - 2.344 4.013 5.219 8.407 0.756

2.448 3.316 4.192 4.116 9.005 7.129

2.820 2.627 4.026 4.516 7.495 0.315

m/se

1.38 9.12 0.36 8.23 9.25 6.08

7.00 7.06 8.41 6.50 9.65

10.13

1.21 1.26 9.48 8.64 9.98

12.22

7.26 10.31 9.55

11.61 13.18

8.41 7.75

10.64 10.41 12.22 - - 6.08

10.17 11.30 13.04 15.24

6.23 9.37

10.97

10.97 13.17 12.78

0.38 6.36

10.49 10.44 12.29 14.58

PI IN/m

2.599 0.095 4.082 4.371 6.405 2.124

2.344 2.408 4.095 4.233 6.343 6.911

2.240 2.661 4.220 4.009 6.584 6.801

2.434 4.592 4.592 6.950 8.680

2.882 2.372 4.641 4.750 6.915

~

~

2.241 4.633 4.771 7.667 9.694

2.220 3.054 4.254 4.302 1.039 6.104

2.558 2.344 4.095 3.985 6.502 6.970

m/se

1.31 8.09 8.20 8.38 9.40 6.96

7.14 1.24 8.36 8.16 9.10

10.13

1.16 7.57 8.25 9.02

10.95 12.95

1.80 10.52 10.21 12.01 13.00

8.36 7.98

10.19 10.14 11.91 ~

~

1.17 10.46 10.44 12.78 13.92

1.49 6.69 9.78

10.06 12.09 11.25

1.65 7.54 9.27 9.25

10.80 12.75

P. klN/m:

2.512 6.041 3.971 4.364 6.426 2.111

2.365 2.409 4.047 4.220 6.309 6.950

2.255 2.661 4.226 4.178 0.686 8.156

2.482 4.466 4.530 6.819 8.329

2.820 2.344 4.323 4.592 6.619

~

~

2.151 4.454 4.399 7.364 0.949

2.141 2.937 4.068 4.137 1.426 6.511

2.530 2.324 4.013 3.041 5.661 8.405

m/.m

1.32 9.01 8.03 8.38 9.41 6.98

1.24 1.29 6.36 0.16 9.80

10.16

7.21 7.65 9.35 9.25

11.20 12.93

8.00 10.26 10.11 11.60 12.65

8.20 1.90 9.53

10.41 11.43 ~

~

7.41 10.13 9.65

12.01 12.95

7.26 8.36 9.40 9.13

11.53 10.90

1.62 1.49 9.09 8.97

10.52 12.01

P, m/m:

2.544 5.985 3.854 4.330 6.350 2.131

2.372 2.402 3.985 4.199 6.281 6.853

2.248 2.689 4.226 4.247 6.122 8.501

2.489 4.289 4.351 6.576 1.917

2.646 2.289 3.999 4.309 6.350

~

~

2.103 4.226 4.109 6.019 8.232

2.082 2.954 3.689 3.999 7.086 6.405

2.530 2.289 3.904 3.737 6.191 8.117

" d e l

1.29 8.99 7.85 8.36 9.45 7.06

7.29 7.32 6.31 0.10 9.00 10.13

1.19 7.80 9.42 9.42

11.35 12.75

8.15 9.86 9.10

11.53 12.24

1.17 7.15 6.69 9.03

11.02 ~

~

1.34 9.70 9.04

11.23 12.04

7.09 8.16 9.02 9.42

11.07 10.64

1.65 1.44 6.99 6.74

10.31 11.73

~

P. IN/m

2.503 5.957 3.130 4.289 6.219 2.186

2.392 2.475 3.875 4.151 0.191 0.118

2.220 2.669 4.109 4.240 6.619 0.156

2.455 4.020 4.130 6.316 7.474

2.511 2.206 3.737 4.002 6.068

~

~

2.062 4.060 3.923 6.401 7.832

2.040 2.785 3.731 3.93c 6.957 6.118

2.511 2.211 3.902 3.102 6.001 1.17C

~

P, IN/m:

2.481 5.881 3.054 4.226 6.191 2.193

2.392 2.461 3.820 4.123 6.164

2.213 2.689 4.033 4.006 8.550 7.911

2.441 3.869 4.020 6.110 1.205

2.413 2.206 3.040 3.944 5.985 - - 2.015 3.965 3.840 5.102 7.612

2.020 2.705 3.602 3.875 6.895 6.136

2.511 2.324 3.985 3.675 6.005 1.688

19

TABLE n.- BURNINGRATE DATA - Concluded

(b) U.S. Customary Units

f -

1.4

P, mia

373 877 576 633 932 307

343 361 587 612 915 008

327 386 613 606 970 270

360 648 657 989 206

409 340 627 666 960

312 646 638 068 298

311 426 590 600 377 953

367 137 I 2 558 121 Zl9

-

CCPL "nil

- 0

- 20

- 40

60

- 80

- 100

- 120

~

140

-

I".

r. 10./5.

0.288 .351 ,316 330 ,373 ,274

0.285 ,287 ,329 ,345 ,386 ,400

0.264 ,301 .368 ,364 ,441 ,509

0.318 .404 ,398 ,467 ,498

0.323 .311 375 .410 ,450

I 0.294 399 ,380 ,473 ,510

0.266 ,330 ,370 ,383 ,454 ,429

0.300 ,295 3 5 8 ,353 ,414 ,473

- - P.

POI,

36! 861 58t 575 61C 274

292 324 558 556 855 956

323 341 502 511 803 920

283 534 543 712 998

354 276 546 496 741 - - 263 504 553 798 981

291 351 503 536 951 782

331 309 528 464 798 968 -

1.6

P. pSLa

369 868 559 628 921 310

344 360 578 609 911 994

326 390 613 616 975 1233

361 622 632 954 1157

384 332 580 625 921

1". ~~

,n./se*

0.278 ,348 ,316 ,297 317 2 4 0

0.238 ,252 ,299 ,308 347 337

0.277 ,255 ,288 ,303 2 5 2 344

0.243 ,335 ,321 ,326 ,393

0.273 .249 .318 ,300 ,343 - - 0.244 ,302 ,327 ,343 ,371

0.264 ,270 310 ,336 ,391 ,350

0.285 2 6 5 ,325 ,303 .352 ,369

m.

r, in./se

0.287 ,354 ,309 ,329 ,372 .278

0.287 2 8 8 .327 ,345 ,388 .399

0.283 307 ,371 ,371 A47 ,502

0.321 ,388 ,385 ,454 .482

0.306 ,305 ,354 ,387 ,434

0.6

P. p51a

382 875 609 615 890 291

331 341 604 595 910 1013

334 367 550 548 645 1150

314 622 596 903 1238

406 315 679 612 1040

329 660 742 1211 1556

357 472 699 697 1344 1114

437 400 708 690 1160 1528

Pr

in.

r, ,n./se

0.289 ,353 2 2 9 ,317 ,351 ,257

0.272 ,271 ,328 ,330 ,374 ,391

0.287 ,278 301 ,326 374 ,441

0.272 .385 3 5 ,417 ,495

0.315 ,286 .399 .372 .483

I 0.307 ,412 .439 .526 .596

0.325 ,362 ,433 .439 .556 .500

0.352 ,346 ,436 ,432 .515 ,585

lanee

1.2

P. 15m

377 884 592 634 929 308

340 361 594 614 920 011

326 386 612 593 955 289

353 666 666 W8 259

416 344 674 689 003

325 672 692 141 406

322 443 617 624 137 984

371 340 594 578 919

301

bum,

in.

r , in./ss

0.290 358 .323 ,330 ,370 2.74

0.281 .285 .329 ,345 ,385 ,399

0.282 .298 ,364 ,355 ,431 ,510

0.311 ,414 ,402 ,473 ,514

0.329 .314 ,401 ,423 ,469

A-

A- 0.306

.412 ,411 .503 ,548

0.295 .342 3 8 5 ,396 .476 .443

0.301 .297 ,365 ,364 ,425 ,502

I

w e and bur

0.8 I". 0.2

P, ,sia

370 837 605 586 828 275

298 326 572 568 868 969

334 343 508 518 632 963

283 556 551 719 008

360 275 565 507 795 -.

271 522 575 884 153

305 368 560 582 167 950

362 336 588 550 992 199

P. 5,:

38: 88' 6 0 62 92 291

331 351 601 60: 92: 021

331 371 561 56: 88: 24:

325 55' 62% 981 29:

421 13: 111 572 133

i4a j98 757 13 1 i60

I 5 5 181 i95 i84 106 121

109 181 171 i55 187 196

1".

r. ,*./*e

0.278 ,337 ,326 .301 ,324 ,241

0.244 ,254 ,307 ,313 3 5 3 372

0.286 ,258 ,293 207 3 6 5 ,362

0.243 ,344 ,327 ,330 ,398

0.278 ,249 ,330 ,307 ,368

I 0.254 ,314 340 ,381 ,437

0.277 ,281 ,346 2 6 5 ,461 ,425

0.290 .291 ,362 ,344 ,438 ,451

tn./se,

0.291 ,359 ,329 ,324 ,364 263

0.278 278 ,331 ,337 ,380 399

0.284 ,286 ,334 ,340 ,393 .481

0.286 ,406 ,376 ,457 ,519

0.331 ,305 ,419 ,410 ,481

NI

NI 0.318 ,424 ,448 ,537 ,600

0.324 369 ,432 ,432 ,542 ,503

0.330 230 .413 .411 ,484 ,574

0.4

P. pSLa

374 853 615 601 860 284

320 336 589 581 890 988

342 358 530 533 828

1036

299 586 575 811 1110

383 291 626 544 945

I

P, ,SI3

381 69: 60: 63' 93: 30:

34: 35% 60: 611 92: 1021

331 37s 59c 561 92:

1283

343 671 657 010 295

431 341 704 699 020 TAB

"AB 337 694 729 198 496

337 466 661 653 225 059

386 354 623 611 W6 405

In.

1,

IO./SP

0.283 -344 .332 209 ,338 ,249

0.262 .263 ,318 221 3 6 4 ,380

0.293 .270 .307 ,317 ,365 ,393

0.258 .362 341 ,373 ,441

0.297 ,264 .366 ,330 A 3 8

n./se

0.290 ,361 ,328 ,330 .370 .268

0.283 ,263 ,331 ,342 ,383 .401

0.286 ,291 ,348 ,347 .415 S O 2

0.300 ,417 ,395 ,472 .524

0.337 ,311 ,417 ,427 .476

A R E

.ARE 0.316 ,424 ,433 ,525 .579

1.308 ,358 ,411 ,413 ,511 ,476

1.312 308 ,368 ,384 ,449 ,501

307 605 673 1122 1462

337 425 657 668 1304 1106

430 395 699 664

1158 1474

0.286 .365 .398 .486 .557

0.306 3 2 5 ,406 ,420 .538 .496

0.345 ,340 ,430 .416 ,513 .564

302 414 564 580 1026 929

361 332 575 542 898 186

0.219 ,322 ,355 .371 .436 ,419

0.301 ,293 ,354 ,344 ,408 ,462

1.8 in.

P, ,Sli

36 86 54 62: 90: 3 1'

3 4 35' 56: 60: 891 98:

32: 391 591 61: 9M 16:

351 58: 595 911 084

361 32c 54: 59: 382 ~

302 j9c 569 340 136

197 104 i41 i70 109 196

165 130 168

i37 162 27

ln./Sel

0.284 ,353 ,301 ,328 367 2 8 5

0.291 ,289 ,323 3 4 3 386 ,399

0.282 ,311 ,365 372 .444 ,490

0.319 ,366 ,368 A40 ,458

0.293 ,294 ,329 368 .418

~ ~~

0.288 ,370 341 .425 .457

0.276 ,316 3 4 3 ,361 ,432 ,406

0.302 .294 3 4 8 ,342 ,402 ,442

1.9 I".

P. p i a

35' 85: 531 61: 891 311

34' 35' 55. 591 894 961

321 3% 581 581 9%

1151

354 5M 583 898 045

350 320 528 572 868

301 578 557 827 104

293 401 534 562 000 890

365 337 576 533 871 115

n./se

0.281 34s .29€ ,324 ,366 ,288

0.291 .288 3 2 1 343 ,387 ,396

0.281 ,313 ,381 353 ,442 ,484

0.319 ,354 ,360 .433 ,445

0.283 .296 3 2 3 357 ,411 - - - -

3.288 3 6 5 334 ,421 A48

1.273 314 ,340 ,363 .430 .403

1.303 ,301 ,356 ,340 ,398 ,438

5 . ,sia

37: 861 58' 611 891 295

331 35c 581 594 891 992

328 377 568 568 892 140

328 611 607 888 143

390 318 616 604 924 259

428 310 618 642 038 279

320 424 600 815 122 969

381 350 607 579 a48 E56

n./se

0.286 ,351 319 ,320 ,355 ,265

0.275 ,276 .321 332 3 7 4 391

0.284 ,287 ,337 3 4 0 ,410 ,446

0.289 ,382 .365 .416 ,465

1.306 .a90 ,368 371 ,432 ,485

1.323 ,292 ,378 ,382 ,457 A92

1.293 3 2 8 ,376 ,390 ,469 .436

1.310 ,306 .374 .365 A24 .486

20

TABLE 111.- BURNING-RATE RESULTS

(a) SI Units

- Burning-rate constants and pressure expunents for distance burned of -

2.54 nini 5.08 mni 10.16 nini \ 15.24 mm 1 20.32 mni I 25.40 nini I 30.48 nini I 35.56 nini 40.64 nini 45.72 mm 48.26 mni _I_-

Accel.

100 120 140

7.42 7.32 7.54 7.77 7.72 7.70 7.02 7.80

.310 8.15 .312

.415 8.61 .413 8.86 .331 1 3 2 1

.366 8.43 .360

.351 8.64 .357

.352 8.53 . .354

.330 8.56 .316

(b) U.S. Customary Units

I -___ Burning-rate constants and pressure exwnents for distance burned of -

0.2 in. 0.4 in. Accel., O.' in. I g units

I I "~__. a,

m./sec

b0.310 .3 10 .337

b.361 .355 ,353 .347 .340

- n I a* 1 n 1 1 n 1 in./sec in./sec in./sec

b0.310 0.245 0.308 0.238 b.321 ,310 b.321 .312 b.341 .415 .330 ,413

.353 ,338 .340 ,328

.336 .366 .332 .360

.340 .351 .340 .357

.337 .352 .336 .354 i' .335 .330 .337 .316

.-

1.257 .316 .424 .354 .366 .364 .354 .352

.331

aNornial into burning surface. bMaxiniuni o r near-maximum values.

L-72-131 Figure 1.- Centrifuge.

S E C T I O N - A A

P E L L

P O R T I GN I

W E I G H T - 1.896 l b (860 (136.7 mm)

Figure 2.- Test motor.

h3 w

inrse c

-

-

-

-

.6(

.5E

.5c

c L - .4f a t z 0 c c 3

.- L

.4c m

.3f

.30

.25 2

mmhec -I 6

I5

I4

I3

12

- 1 1

I I I I 1 1 1 1 400 6 00 800 IO00 1200 1400 1600 psia

- 10

-9

-8

-7

'6 I 2 4 6 8 IO 12 MN/m2

Pressure , p

Figure 3.- Typical burning-rate data a t 140g normal acceleration. Solid symbols denote single test.

24

6.0 -

1.0

5.0 -

-

4.0 - !+

2.0 -

Time, sec

Figure 4.- Typical chamber pressure histories as a function of acceleration for 5.08-cm (2.0 in.) web motors. N Ln

1.25

1.20

0 L \ L

C

c, a c, C a,

.: 1.15

k 3 lu a, c, a t 1.10 OI C

C L 3

.r

m

1.05

1 .oo

0 Average burning r a t e 0 Maximum burning r a t e

Normal a c c e l e r a t i o n , g u n i t s Figure 5.- Effect of acceleration on average and maximum burning-rate augmentation for 5.08-cm (2.0 in.)

web motor. Pressure, 3.45 MN/m2 (500 psia).

.5!

.5(

.4

c L k .41 z +

m

'

'

'

Pressure psia MN,"~

0 300 2.07 600 4.14

0 900 6.21 A I200 8.27

0 c .- E m 3

.35

-30

-25

u u 0 0 u o A

-

-

-

sec 4

3

2

I

0

3

3

7

3

I I I I I I I I I I I C2O0 .2 .4 .6 .8 I .o 1.2 1.4 I .6 1.8 2.0in.

I I -1 I I 1 I I I I I I 1 I

0 4 8 12 16 20 24 28 32 36 40 44 48 52" Distance burned ,DB

(a) Og normal acceleration.

Figure 6.- Instantaneous burning-rate data.

27

inisec .55

.50

.45

.40 0) + z E m

0 c .-

3

.35

.3 0

mmisec

Pre s s ure psia MN/m2

0 300 2.07 0 600 4.14 0 900 6.21 A 1200 8.27

A a

,. V V

r - A

"

---9

---P

n v V v U

I I I I I I 1.8 2.0in. I .6 0 .2 .4 .6 .0 1.0 1.2 1.4

I I I I I I I 1 I I I 1 1 I


(b) 20g normal acceleration.

Figure 6. - Continued.

28

in/sec mm/ sec

I / A

L I / l3 c c 3

._ I

m

" - --P

- -P

-*! I psia MN/mL 0 300 2.07

600 4.14 0 900 6.21

14

13

12

II

IO

9

8

7

6

A 1200 8.27

.4 .6 .8 I .o 1.2 I .4 I .6 1.8 2.0in. I I I I 1 I I I I .20 I t ~

0 .2 1 1 I 1 1 I - 1 I I I . -1 I 1 I 0 4 8 12 16 20 24 28 32 36 40 44 48 52"

Distance burned ,DB

(c) 40g normal acceleration.


29

in/sec mm/sec

.55

.50

.45

c &. .40

e a c

0 c C ._ L

.35 m'

.30

.25

.20

---p

--P #-

d W

- -P Pressure psia MN/m2 300 2.07 600 4.14 900 6.21 1200 8.27

14

13

12

II

IO

9

8

7

s

I I AI-' I-L-L..I- A

.2 .4 .6 .8 I .o I .2 I .4 I .6 1.8 2 .0 in . I I I I _ 1 - 1 1 -1 1 ..I I I I J

0 4 8 12 16 20 24 28 32 36 40 44 48 52mm Distance burned ,DE

(d) 60g normal acceleration.


30

in/sec 5 5

50

.45

c L

al 0

0 c

- .4c c

L

.- E

.3: 2

.3c

.2f

.2(

mi

1 ---P

_ _ -

I

.2 I 1 I

0 4 8

psia MN/m' 0 300 2.07 0 600 4.14 0 900 6.21 A I200 8.27

sec 1

3

2

1

0

3

3

7

3

I 1 1 1- I --a -A. I _ - 1 .6 .8 I .o I .2 1.4 1.6 1.8 2 Oin

12 16 20 24 2 8 2 36 40 44 48 52" I 1 1 - ' 1-

.4- I I _ _ I

Distance burned ,DB

(e) 80g normal acceleration.

Figure 6.- Continued.

31

I

inbec mm/sec .5

.5

.4!

.4 (

.3:

.3c

.25

.20

- ---P

--P

U A n

---P Pressure psia M N , ~

0 300 2.07 0 600 4.14 0 900 6.21 A 1200 8.27

I I I I I I I I I ~~ 1

.2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 in.

14

13

12

I1

io

3

3

?

I

I I I I I b 1 I I I I I I I

0 4 8 12 16 20 24 28 32 36 40 44 48 52"

Distance burned ,DB

(f) l O O g normal acceleration.


32

iryse c .55

.50

.45

L

L. .4c

P

E m

0) +

0 c .- 3

.3f

.3c

.2:

.2(

---P

3 ---

Pressure psia M N / ~ ~

0300 2.07 0600 4.14 0900 6.21 A1200 8.27

-

---P

I I I I I I I I 1 I 1.8 2.0 in. .2 .4 .6 .8 I .o 1.2 1.4 1.6

I I I I I 1 1 1 1 - I I I I I


(g) 120g normal acceleration.


33

mm/sec in/sec

-

-

-

.5!

.5(

.4f

L+ - .4c al + 2 0 - 8 K c L 3

.-

D .3E

.30

.25

- 14

- 13

12

II

IO

- 9

- 8

-7

----+++

---P

.20

-7 J

I I I I I I I .-

4 J

b ---P

/ Dsia MN/& 0 300 2.07 0 600 414 0 900 6.21 A1200 827

n

---P

1, ' . I - I

I .6 1.8 2.0 in.

40 44 48 52 m m 1 1 . 1 1

34

in/: .5!

.5(

.4!

t .4(

e

E m 3 !

Q +

CI, c

3

.-

.3 (

.2!

.2(

mm/sec 4

3

2

I

0

3

3

7

3

_~. . .2 .4 .6 .a I .o 1.2 I .4 1.6 1.8 2.0 in.

I I I I ~ 1 ~ - 1 I I I I I I I 1

0 4 8 12 16 20 24 28 32 36 40 4'4 48 52 mm Distance burned, DB

Figure 7. - Composite instantaneous burning-rate data at nominal chamber pressures of 4.14 MN/m2 (600 psia).

35

in/sec I .5

.5'

.4

c .4(

W c z E m

m c ._

3

.3!

.3(

.2!

A n

0 ,. 0

0

Pressure psia MN/m2

0 300 2.07 0 600 4.14 0 900 6.21 A 1200 8.27

.2c 0 20 40 60 80 100 120 140

Normal acceleration, g units

Figure 8.- Effect of acceleration on rt,max.

isec 4

3

2

1

3

1

36

i n .

2 .0 , - Pressure

p s i a MN/m 2

0 300 2.07 0 600 4.14 0 900 6.21 A 1200 8.27

Normal a c c e l e r a t i o n , g u n i t s

Figure 9.- Distance burned to rt,max as a function of normal acceleration.

w 4

mm

3 52

- 48

- 44

- 40 - 36

- 32

- 24

- 20

-~16

-12 i:

in/sec

- 8

- 7

mmisec .5

.5

.4

c L

al 0

cn C C 3

- .4( c

L

._ L

.3' m

.3 (

.2!

.2(

- n 0 0

U U

'I 'I

Pressure psia M N , ~ ~

0 300 2.07 0 Quasi-equilibrium rate 0 600 4.14 $) Decreasing rate 0 900 6.21 A 1200 8.27

I I I I I I

20 40 60 80 100 120 140 Normal accelerat ion, g units

Figure 10.- Instantaneous burning rate a t DB = 48.3 mm (1.9 in.) as a function of normal acceleration.

38

W 42 la L

p s i a

2 M N / m

Pressure, p

Figure 11.- Effect of pressure on maximum burning-rate augmentation at 140g.

39

cp 0

.4

e%& 0 O h

0 O/O 0 O h 2 5 '/o Oo/o Buttons

0% 0 O/O 4% 28% Irregular

0% Sheets 0 O/O 0 O h 0 O/O

4.27 OI

0 \ cn

0 E

I I I I 0 12.7 2 5.4 38.1 50.8 mm

I

Web thickness

(a) 20g normal acceleration.

Figure 12.- Effect of propellant thickness on residue weight at nominal chamber pressures of 4.14 MN/m2 (600 psia).

0 O/O 0 O/O 0 O/O 0'10 Butt on s

4 2 % 0 O h 3 % 2 YO Irregular

0 O/O 0 O/O 0 OXJ 0% Sheets

1.0

-8

.6

.4

.2

0

10.7

8.54

6.41

4.27

2.14

0

I I

0 12.7 2 5.4 38.1 I I I

50.8 mm W e b t h i c k n e s s

(b) 40g normal acceleration.


2 .o

1.5

1.0

.5

0

0 O/O 0 O/O 2 5 O/O 34% Buttons

0% I 0% 0 O/O 0% Irregular

0 O/O 0% 0% 0% Sheets

21.4

16.0

10.7

’ 5.34

I I I 0 1.0 I .5 2.0 in. .5

I I I I I 12.7 25.4 38.1 50.8 mm 0

Web t h i c k n e s s

(c) 60g normal acceleration.


0% Sheets 0 % 0 % 0%

-1 4.27

(d) 80g normal acceleration.


O0/o Spheres

3 I O/o 27% Buttons 0 O/O 6 '/o

0 O/O 2 O/O 9%

I 6 0% 0% 32% Sheets

I I I I

0 12.7 25.4 50.8 I mm

38.1 Web th ickness

(e) lOOg normal acceleration.


L

*& 0 O/O 0% Spheres

8.0 1 I I

14% But tons 0% I 8 '/o

8.54 )

(u

0 E

0 O h I 8 O/o 0% Irregular 0%

0 O/O 0% 3 9 '/o

0 O/O 0% 0% Spheres

0 O/O 2 0 O/O 5% Buttons

0 O/O 5 O/O 0 O/O O X Irregular

5 O/O 0 O/O @ Sheets

20.0

16.0

12.0

8.Q

4 .O

0 I

I

i

21.4

17. I

12.8

8.54

4.27

0 3 in.

I I I I I 0 12.7 25.4

W e b th ickness

(g) 140g normal acceleration.

Figure 12.- Concluded.

38.1 50.8 mm

2 0% 0% 0% Ooh Spheres

0% 2% 3 4% 2 7% 14% 5% Buttons P -

2 8% 0% 0% 32% (qlo$ 0% O% Irregular \ /

0 O/O 0 O/O 0% 0 Oh 32% @ Sheets

16.0 tl7.l $ I /I 3 ..

(u

12.8 2 X

12.0

Normal acceleration, g units

Figure 13.- Effect of normal acceleration on 5.08-cm (2.0 in.) web motor residue weight at nominal chamber pressures of 4.14 MN/m2 (600 psia).

10

IO.(

0,

+ c 0, .- !$ I.0C

a, 3 U u) .- ?!

e s! a

0) 0

.IO

.o I I

Normal acceleration, g units 0 0 0 A b n n

.20 40 60 80 100 120 140

~

.5 1.0 1.5 2

1.07~ I@

-07 x IO-'

cu E V \ 0

W 3 -0 fn ._

E V

Y- O a,

._

a (I)

1.07~ 10-3

. 0 7 ~ 1 0 - ~ 1 in.

1 I I I -1

2 5.4 38.1 50.8 mm 0 12.7 Dis tance burned, DB

Figure 14.- Average residue weight as a function of distance burned with acceleration as a parameter.

48

20.0

10.0

0

r 0 W

+

.- 3 W ; 1.c .- v) z

e 2

W 0,

a /

/ / /

20 40 60 80 100 I: Normal acceleration, g units

Figure 15.- Average residue weight as a function of normal acceleration for 5.08-cm (2.0 in.) web motor at nominal chamber pressures of 4.14 MN/m2 (600 psia).

49

01 0

1 I I I I I I 1490 p s i a 200 400 600 800 1000 1200

I I I I I I I I I I 0 1 2 3 4 5 6 7 8 9 l’0 MN/m2

Pressure , p Figure 16.- Effect of pressure on residue weight at 140g normal acceleration.

I

Static7DB=l.0in.(25.4mm),t =3.0sec 40g,DB=1.5in.(38.1 mm), t = 5.0sec Bimodal

609, DB=I.Oin.(25.4mm 1, t 2.75 sec

lOOg ,DB=0.8 in.(20.3mm ),t= 2.0sec I20 g , DB= 0.6 in.(15.2mm) t I. 5 se c

25.4" (I.Oin.1

Figure 17.- Photographs of extinguished propellant surface at time of maximum burning rate for various normal accelerations.

I I' -1 L-72-132

51

.

120-

100 ’

80 . I

~

140 Normal acce le ra t ion , g units

Figure 18.- Effect of acceleration on pit diameter and pit density at maximum Throat sized for nominal chamber pressure of 4.14 MN/m2 burning rate.

(600 psia).

52

cn w

2 0

psia

8 0 0.-

0.-

0-

600.-

0 I 2 3 4

T i m e , s e c

Figure 19.- Extinction test pressure histories at 140g.

5 6

. .

Stat ic ; DB=I.Oin.(25.4 mm) DB =0.24in.(6.1 mm) ;0.75sec Rise

DB = 0.39 in.( 9.9 mm) ; 1.25se c DB= 0.78 in.(l9.8mml ; 2.00 sec Peak Decay

DB=1.16in.(29.5mm); 3.00 sec DB=t.52in.(38.6mm) ; 4 . 0 0 s e c

Decay 25.4" Equi ti brium (I .O in. )

L-72-133 I-----+

Figure 20.- Photographs of extinguished propellant surface at 140g and pressures shown in figure 19.

54

I

0

10

cu 5 - \ m c, Q .r

10 >s c, .r m - 3 S al -0

c, .r a

0

'in.

Q

- 6

- 5

z 4 L aJ c, aJ E .r -u c,

Q

c m al E L

.r

- 2 x 5 z

- 1

0

0 P i t d iamete r 0 P i t d e n s i t y

I I I .I .5 1 .o 1.5 2.

I 1 I I 12 24 36 48 mm

Dis tance burned, DB

Figure 21.- Effect of distance burned on pit diameter and pit density at 140g normal acceleration and nominal chamber pressure of 4.14 MN/m2 (600 psia).

55

c L c

Q 0 c

0 c .- E

m' Ill-

10 -

9-

8 -

7-

A5 -

.40 -

.35 - 80% Sheets

.30 - 95% Buttons

I _ _ ! ~

0 .5 1.0 I .5

6

4

2

0 2.0 in.

I I - . .. . . ~ ~ . - r_ I I 0 12 24 36 48 mm

Distance burned , OB

Figure 22. - Correlation of burning-rate and residue characteristics.

56 NASA-Langley, 1972 - 33 L-7847

NATIONAL AERONAUTICS AND SPACE ADMISTRATION WASHINGTON, D.C. 20546

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Effects of normal acceleration on transient burning-rate ...

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